Distribution of PageRank Mass Among Principle Components of the Web

Avrachenkov, Konstantin; Litvak, Nelly; Pham, Kim

doi:10.1007/978-3-540-77004-6_2

Cited by 20 publications

(19 citation statements)

References 23 publications

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“…It has been noted before in Boldi et al (2005) and Avrachenkov et al (2007); but the proof of this result is particularly simple here, since we simply combine known results about the location of dominant SCCs from Berman and Plemmons (1979) with our Theorem 1.…”

Section: Normalizationmentioning

confidence: 78%

Eigenvectors of directed graphs and importance scores: dominance, T-Rank, and sink remedies

Bjelland

Burgess

Canright

et al. 2009

Data Min Knowl Disc

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We study the properties of the principal eigenvector for the adjacency matrix (and related matrices) for a general directed graph. In particular-motivated by the use of the eigenvector for estimating the "importance" of the nodes in the graph-we focus on the distribution of positive weight in this eigenvector, and give a coherent picture which builds upon and unites earlier results. We also propose a simple method-"T-Rank"-for generating importance scores. T-Rank generates authority scores via a one-level, non-normalized matrix, and is thus distinct from known methods such as PageRank (normalized), HITS (two-level), and SALSA (two-level and normalized). We show, using our understanding of the principal eigenvector, that T-Rank has a much less severe "sink problem" than does PageRank. Also, we offer numerical results which quantify the "tightly-knit community" or TKC effect. We find that T-Rank has a stronger TKC effect than PageRank, and we offer a novel interpolation method which allows for continuous tuning of the strength of this TKC effect. Finally, we propose two new "sink remedies", i.e., methods for ensuring that the principal eigenvector is positive everywhere. One of our sink remedies (source pumping) is unique among sink remedies, in that it gives a positive eigenvector without rendering the graph strongly connected. We offer a preliminary evaluation of the effects and possible applications of these new sink remedies.

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Section: Normalizationmentioning

confidence: 78%

Eigenvectors of directed graphs and importance scores: dominance, T-Rank, and sink remedies

Bjelland

Burgess

Canright

et al. 2009

Data Min Knowl Disc

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“…α denotes the probability that the surfer will follow one of the links in the current page while (1−α) is the probability that the surfer will jump to a page that is not necessarily linked by the current page. Again, this is the mathematical representation of the solution presented in can be further tuned using feedback obtained from external sources [4,23]. The t = (t i ) vector is referred to as the teleportation vector, where t i indicates the probability of jumping to page i.…”

Section: Pagerank Definitionmentioning

confidence: 99%

“…3.3). Regarding the first possibility (customizing the random jump probability), several works investigated the effect of α on the quality of the final rankings [4,23,24,25]. The order of pages in the final PageRank vector is found to be heavily affected by the α constant used [25].…”

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confidence: 99%

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Incorporating the surfing behavior of web users into pagerank

Ashyralyyev

Cambazoğlu

Aykanat

2013

Proceedings of the 22nd ACM International Conference on Information &Amp; Knowledge Management

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One of the most crucial factors that determines the effectiveness of a large-scale commercial web search engine is the ranking (i.e., order) in which web search results are presented to the end user. In modern web search engines, the skeleton for the ranking of web search results is constructed using a combination of the global (i.e., query independent) importance of web pages and their relevance to the given search query. In this thesis, we are concerned with the estimation of global importance of web pages. So far, to estimate the importance of web pages, two different types of data sources have been taken into account, independent of each other: hyperlink structure of the web (e.g., PageRank) or surfing behavior of web users (e.g., BrowseRank). Unfortunately, both types of data sources have certain limitations. The hyperlink structure of the web is not very reliable and is vulnerable to bad intent (e.g., web spam), because hyperlinks can be easily edited by the web content creators. On the other hand, the browsing behavior of web users has limitations such as, sparsity and low web coverage.In this thesis, we combine these two types of feedback under a hybrid page importance estimation model in order to alleviate the above-mentioned drawbacks. Our experimental results indicate that the proposed hybrid model leads to better estimation of page importance according to an evaluation metric that uses the user click information obtained from Yahoo! web search engine's query logs as ground-truth ranking. We conduct all of our experiments in a realistic setting, using a very large scale web page collection (around 6.5 billion web pages) and web browsing data (around two billion web page visits) collected through the Yahoo! toolbar.

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“…From a computational perspective, as α → 1, the number of iterations till convergence to the PageRank vector grows prohibitively, and also makes the computation of the rankings numerically ill-conditioned [11,12]. Moreover, from a qualitative point of view, various studies indicate that damping factors close to 1 result into counterintuitive ranking vectors where all the PageRank gets concentrated mostly in irrelevant nodes, while the Web's core component is assigned null rank [1,4,5,13]. Finally, the very existence of the damping factor and the related teleportation matrix "opens the door" to direct manipulation of the ranking score through link spamming [6,8].…”

Section: Introductionmentioning

confidence: 99%

Random Surfing Without Teleportation

Νικολακόπουλος

Garofalakis

2015

Algorithms, Probability, Networks, and Games

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Abstract. In the standard Random Surfer Model, the teleportation matrix is necessary to ensure that the final PageRank vector is well-defined. The introduction of this matrix, however, results in serious problems and imposes fundamental limitations to the quality of the ranking vectors. In this work, building on the recently proposed NCDawareRank framework, we exploit the decomposition of the underlying space into blocks, and we derive easy to check necessary and sufficient conditions for random surfing without teleportation.

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Distribution of PageRank Mass Among Principle Components of the Web

Cited by 20 publications

References 23 publications

Eigenvectors of directed graphs and importance scores: dominance, T-Rank, and sink remedies

Eigenvectors of directed graphs and importance scores: dominance, T-Rank, and sink remedies

Incorporating the surfing behavior of web users into pagerank

Random Surfing Without Teleportation

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